| 1. Foundations |
Mathematical Foundations & Set Theory |
- Calculus & Linear Algebra fundamentals.
- Set Theory & Venn Diagrams.
- Counting: Permutations, Combinations.
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- Build the necessary mathematical knowledge.
- Solve basic counting problems.
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| 2. Probability Core |
Basic Concepts of Probability |
- Sample Space, Events.
- Definitions of Probability: Classical, Statistical.
- Conditional Probability, Bayes' Theorem.
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- Delve into the first principles of probability theory.
- Apply Bayes' theorem to solve problems.
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| 3. Distributions |
Random Variables & Probability Distributions |
- Discrete & Continuous Random Variables.
- Probability Density Function (PDF) & Cumulative Distribution Function (CDF).
- Expectation, Variance, Standard Deviation.
- Common Distributions: Binomial, Poisson, Normal.
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- Model the random outcomes of an experiment.
- Calculate key metrics of distributions.
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| 4. Multiple Variables |
Joint Probability Distributions |
- Joint & Marginal Distributions.
- Covariance, Correlation Coefficient.
- Central Limit Theorem (CLT).
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- Study the relationships between multiple random variables.
- Understand the importance of the CLT.
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| 5. Statistics Intro |
Introduction to Statistics |
- Descriptive Statistics: Mean, Median, Variance...
- Data Visualization: Histograms, Box Plots.
- Inferential Statistics: Population & Sample.
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- Begin the journey from theory to practical data analysis.
- Summarize and visualize datasets.
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| 6. Inference |
Parameter Estimation & Hypothesis Testing |
- Point Estimation: MLE Method.
- Confidence Intervals for Mean & Proportion.
- Hypothesis Testing: Null (H₀) & Alternative (Hₐ), p-value.
- Common Tests: Z-test, t-test, Chi-squared.
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- Estimate population characteristics from sample data.
- Use data to make decisions about claims.
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| 7. Modeling |
Linear Regression |
- Simple & Multiple Linear Regression.
- Ordinary Least Squares (OLS).
- Model Evaluation: R-squared Coefficient.
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- Model the relationship between variables.
- Build and evaluate simple predictive models.
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| 8. Advanced & Applied |
Advanced Topics & Tools |
- Analysis of Variance (ANOVA).
- Bayesian Statistics.
- Markov Chains & Monte Carlo Simulation.
- Applications in Data Science, Machine Learning, Finance.
- Tools: Python (NumPy, Pandas, SciPy) & R.
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- Explore more specialized areas.
- Apply knowledge to practice with real-world datasets.
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